Question

1.There are 10 kids running a race. How many ways are there for them to come in first, second, and third place?

2.In a drawing, a jar holds the numbers 1 to 8. If you draw three numbers to form a three-digit number (without replacement), what is the probability you will draw 135?

Answer 1

1: 720

2:
`(1)/(336)`

Explanation:

1: There are 10 kids in a race so the number of ways such that they come first , second and third=10×9×8

=720

(since the first place is occupied by any one of the ten students i.e. we have ten choices after occupying first position there are only 9 students left for second position and after occupying second for the third position only 8 choices are left)

2: We have to find the probability such that there is no replacement such that we draw 135.

for the first position we have to find the probability(
`P_(1)`) that '1' comes out of 8 numbers=
`(1)/(8)`

similarly for second choice we could not take 1 as there is no replacement

so probability that 3 comes(
`P_(2)`) =
`(1)/(7)`

similarly probability that 5 comes at third position(
`P_(3)`) =
`(1)/(6)`

hence, probability that 135 is drawn=
`(1)/(8)*(1)/(7)*(1)/(6)=(1)/(336)`

Answer 2

1. 10 x 9 x 8 = 720
There are 720 ways for them to come in first, second and third place.
2. Probability = 1/8 x 1/7 x 1/6 = 1/336
The probability is 1/336 or 0.002976.